The former River Plate, Barcelona and AC Milan forward fired the winner midway through the first half after playing a one-two with Eder as Sampdoria continued to pull clear of the danger zone.
The fixture was moved to Monday evening after both Genoa and Sampdoria fans threatened to boycott the match in protest at the original Sunday midday kickoff time.
The boycott was called last week by the hardcore "ultra" fans of both clubs.
Sampdoria are 13th with 25 points, having won four and drawn four out of 10 games since former Serbia coach Sinisa Mihajlovic took charge of the side in November.
Genoa, who have also enjoyed a revival under Gian Piero Gasperini, are two points and two places above their rivals.